How can i merge these two meshes without non manifold edges?
There are several ways you can go about doing this. If the two patterns must be part of one mesh for your purposes, the use the second two options, but if they don't need to be merged into one, then first option will probably work better in the long run and is nondestructive.
Parenting the Meshes
First, if you don't need the objects to actually be a part of the same mesh, you can parent one to the other. This will allow them to be transformed, keyframed, and animated as one object, but won't cause the problems of non-manifold geometry. This approach may also make texturing easier. You can parent them by selecting one mesh, hold shift and select the other. Then press ctrl+P and set parent to object.
Merge and Manual Editing
If the objects need to be part of one mesh, you can join them by selecting one mesh, hold shift and select the other. Then press ⌘+J to join the meshes. Once complete, you can go into Edit mode, ensure you have Vertex Select enables, and go to Select &gt; Select All by Trait &gt; Non Manifold. This will identify any Non Manifold geometry in you mesh and you may be able to fix it by hand.
Merge and Remeshing
You can also try remeshing the object once merged. Go to the Sculpting window and locate the Remesh option near the top. You can adjust the size of the new faces from here (based on Voxel Size). The smaller the Voxel Size, the more detailed the new mesh will be, but it will also take longer and create and object with many more vertices. This approach may also cause unwanted geometry between the two objects.
As mentioned previously, the first approach will most likely yield the most desirable results.